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Galois Theory

  • Textbook
  • © 1990

Overview

Authors:
  1. Joseph Rotman

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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Part of the book series: Universitext (UTX)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Galois Theory

    1. Rings

      • Joseph Rotman
      Pages 1-7

    2. Homomorphisms and Ideals

      • Joseph Rotman
      Pages 7-9

    3. Quotient Rings

      • Joseph Rotman
      Pages 10-11

    4. Polynomial Rings over Fields

      • Joseph Rotman
      Pages 12-17

    5. Prime Ideals and Maximal Ideals

      • Joseph Rotman
      Pages 17-20

    6. Finite Fields

      • Joseph Rotman
      Pages 20-22

    7. Irreducible Polynomials

      • Joseph Rotman
      Pages 22-25

    8. Classical Formulas

      • Joseph Rotman
      Pages 25-28

    9. Splitting Fields

      • Joseph Rotman
      Pages 28-33

    10. Solvability by Radicals

      • Joseph Rotman
      Pages 33-35

    11. The Galois Group

      • Joseph Rotman
      Pages 35-38

    12. Primitive Roots of Unity

      • Joseph Rotman
      Pages 38-41

    13. Insolvability of the Quintic

      • Joseph Rotman
      Pages 41-42

    14. Independence of Characters

      • Joseph Rotman
      Pages 43-46

    15. Galois Extensions

      • Joseph Rotman
      Pages 46-48

    16. The Fundamental Theorem of Galois Theory

      • Joseph Rotman
      Pages 48-50

    17. Applications

      • Joseph Rotman
      Pages 50-53

    18. Galois’s Great Theorem

      • Joseph Rotman
      Pages 54-56

    19. Discriminants

      • Joseph Rotman
      Pages 56-58
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Keywords

About this book

This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom.

Authors and Affiliations

  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Joseph Rotman

Bibliographic Information

  • Book Title: Galois Theory

  • Authors: Joseph Rotman

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4684-0367-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1990

  • Softcover ISBN: 978-0-387-97305-0Due: 06 December 1994

  • eBook ISBN: 978-1-4684-0367-1Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 108

  • Topics: Group Theory and Generalizations

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